Simplify the following expression: $ y = \dfrac{-4}{9} + \dfrac{5k + 1}{-9k} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9k}{-9k}$ $ \dfrac{-4}{9} \times \dfrac{-9k}{-9k} = \dfrac{36k}{-81k} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{5k + 1}{-9k} \times \dfrac{9}{9} = \dfrac{45k + 9}{-81k} $ Therefore $ y = \dfrac{36k}{-81k} + \dfrac{45k + 9}{-81k} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{36k + 45k + 9}{-81k} $ $y = \dfrac{81k + 9}{-81k}$ Simplify the expression by dividing the numerator and denominator by -9: $y = \dfrac{-9k - 1}{9k}$